three numbers are in the ratio of 3:4:5 and their LCM 2400.Thier HCF is
Answer (1)
Student Expert
21st Dec, 2020
Hi
Given ratio = 3:4:5
So,
Let us assume that the numbers are 3x, 4x and 5x.
Then,
their lcm = 60 x .
Now, it is given that lcm = 2400
Then,
60 x = 2400
or x = 40.
The numbers are
(3 x 40) = 120 = 2^ 3 x 3 x 5
(4 x 40) =160 = 2^5 x 5
(5 x 40)=200 = 2 ^3 x 5^2
Then,
HCF = 2^3 x 5 = 8 x 5 = 40
Hence, H.C.F. = 40.
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